Dispenser closures that open by the axial movement of a closure along a container neck are generally known in the art. Such a closure commonly includes a closure portion that is threadably attached to the neck of a container in such a way that the closure may be threadably moved from a closed position to an open position so as to access the contents of the container. The closure of this type of closure commonly has a limited range of rotation, so that the closure may remain affixed to the container even while in the open position (i.e. non-removable). Typically, these closures do not have a child resistant feature.